We describe the rank 3 Temperley-Lieb-Martin algebras in terms of Kuperberg's A2-webs. We define consistent labelings of webs and use them to describe the coefficients of decompositions into reduced webs. We introduce web immanants, inspired by Temperley-Lieb immanants of Rhoades and Skandera. We show that web immanants are positive when evaluated on totally positive matrices and describe some further properties.
- Temperley-Lieb-Martin algebra
- Total positivity